![\[\left( \mathbf{i} \right)~\psi \text{ }\left( x \right)\text{ }=\text{ }cos\text{ }\left( 3x \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-203d024ba4c0ad87e16a6859ecfd38f6_l3.png "Rendered by QuickLaTeX.com")
Since,
![\[f\text{ }\left( x \right)\text{ }=\text{ }cos\text{ }x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-232ee4244165606f5ff6da8b7bed8a34_l3.png "Rendered by QuickLaTeX.com")
is a periodic function with period
![\[2\pi .\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-313cee50ad08035288583dd75ddb82f4_l3.png "Rendered by QuickLaTeX.com")
Therefore,
![\[\psi \text{ }\left( x \right)\text{ }=\text{ }cos\text{ }\left( 3x \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b2a1b4134973a796c6635ab0b84e14c4_l3.png "Rendered by QuickLaTeX.com")
is a periodic function with period
![\[2\pi /3.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d4040f3c950ee5d3bb174507d8d03b5c_l3.png "Rendered by QuickLaTeX.com")
Hence, we draw the graph of
in the interval
![\[\left[ 0,\text{ }2\pi /3 \right].\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-74c06ec4584e1fa78ac40f51975654f0_l3.png "Rendered by QuickLaTeX.com")
The values of
at various points in
![\[\left[ 0,\text{ }2\pi /3 \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-19bc972f79a63bbb53bf6d2316e3c747_l3.png "Rendered by QuickLaTeX.com")
are listed below:
The curve is:
![\[\left( \mathbf{ii} \right)~u\text{ }\left( x \right)\text{ }=\text{ }co{{s}^{2}}~x/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5d2d1824f2a12b060abf90f7dd4b5bd8_l3.png "Rendered by QuickLaTeX.com")
Since,
is a periodic function with period
Therefore,
![\[u\text{ }\left( x \right)\text{ }=\text{ }co{{s}^{2}}~\left( x/2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-22b445c92136afc1158a6ac12d724571_l3.png "Rendered by QuickLaTeX.com")
is a periodic function with period
![\[\pi .\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c2862ad18f71a9ca9dc702696fb19c96_l3.png "Rendered by QuickLaTeX.com")
Hence, we draw the graph of
in the interval
![\[\left[ 0,\text{ }\pi \right].\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dde5082b7e75cc46f27d9a95f99e0305_l3.png "Rendered by QuickLaTeX.com")
The values of
at various points in
![\[\left[ 0,\text{ }\pi \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9ad7b2422aef6503ec2245c9b5d8b452_l3.png "Rendered by QuickLaTeX.com")
are listed below:
The curve is:
